Editing Logarithmic form (section)

===Logarithmic differentials and singular cohomology===
Let ''X'' be a complex manifold and ''D'' a divisor with normal crossings on ''X''. Deligne proved a holomorphic analog of de Rham's theorem in terms of logarithmic differentials. Namely,
:<math> H^k(X, \Omega^{\bullet}_X(\log D))\cong H^k(X-D,\mathbf{C}),</math>
where the left side denotes the cohomology of ''X'' with coefficients in a complex of sheaves, sometimes called [[hypercohomology]]. This follows from the natural inclusion of complexes of sheaves
:<math> \Omega^{\bullet}_X(\log D)\rightarrow j_*\Omega_{X-D}^{\bullet} </math>
being a [[quasi-isomorphism]].<ref>Deligne (1970), Proposition II.3.13.</ref>